Ordinary Annuity:An Ordinary Annuity has the following characteristics:

The payments are always made at the end of each interval

The interest rate compounds at the same interval as the payment interval

For calculating the sum of a series of regular payments the following formula should be used:

R[(1+i)^ n -1] S n = —————– i

Example: Alan decides to set aside $50 at the end of each month for his child’s college education. If the child were to be born today, how much will be available for its college education when s/he turns 19 years old? Assume an interest rate of 5% compounded monthly.

Solution:First, we assign all the terms:

R= $50i= 0.05/12 or 0.004166n= 18 x 12, or 216

Now substituting into our formula, we have:

R[(1+i)^n-1] S n = ——————- i

$50[(1+0.05/12)^216 -1] S n = ——————————– 0.05 / 12

S n = $50(349.2020206)

S n = $17,460.10

Formula for calculating present value of a simple annuity:

R[1-(1+i)^-n] A n = ——————– i

Example: Alan asks you to help him determine the appropriate price to pay for an annuity offering a retirement income of $1,000 a month for 10 years. Assume the interest rate is 6% compounded monthly.

Solution:Substituting into our formula, we have:

R = $1,000 i = 0.06 /12 or 0.005 n = 12 x 10, or 120

$1,000[1-(1+0.005)^-120]A n = ———————————– 0.005

A n = $90,073.45

Annuity Due:In an annuity due, the payments occur at the beginning of the payment period.

For calculating the sum of a series of regular payments the following formula should be used:

R(1+i)[(1+i)^ n -1] S n (due)= ———————– i

Example: Alan wants to deposit $300 into a fund at the beginning of each month. If he can earn 10% compounded interest monthly, how much amount will be there in the fund at the end of 6 years?

Example: The monthly rent on an apartment is $950 per month payable at the beginning of each month. If the current interest is 12% compounded monthly, what single payment 12 months in advance would be equal to a year’s rent?

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